Hollow fiber (HF) membranes that have a higher packing density than conventional flat sheet membranes and which readily permit backwashing are widely used in many applications. The pore sizes of microfiltration (MF) HF membranes range from 0.05 to 5 μm and those for ultrafiltration (UF) HF membranes range from 5 nm to 50 nm. Since the pore-size distribution (PSD) of membranes can greatly affect membrane performance, the PSD of HF membranes needs to be accurately characterized.
The PSD of UF membranes can be determined via direct observation methods such as scanning electron microscopy (SEM) and atomic force microscopy (AFM). SEM requires a high vacuum and therefore drying the sample, which can alter the pore structure. In order to minimize charging and damage due to the electron beam, non-conducting samples have to be conductively coated; this can decorate the membrane pores and alter the PSD. Field-emission SEM (FESEM) can reduce the charging and electron beam damage by being able to use a lower voltage. Environmental SEM (ESEM), developed for wet or non-conducting materials, avoids having to coat or dry the samples. However, lower resolution limits its use for characterizing UF membranes. AFM scans the sample surface with a fine tip on a cantilever whose deflections are used to generate a three-dimensional (3D) map of the surface topography. AFM does not require special sample preparation and can be done in a gas or liquid. It can determine the pore size, surface porosity, and PSD of a membrane. However, direct characterization methods image a small area (typically <1 mm2) that might not be representative of the membrane on the macroscale. Furthermore, direct observation methods that include scanning electron microscopy (SEM), field-emission scanning electron microscopy (FESEM), environmental scanning electron microscopy (ESEM), and atomic force microscopy (AFM) require very expensive instruments that are limited in that they can measure the pore size only within a small area of a few hundred microns. Moreover, they are of limited use for obtaining the PSD of irregular pores such as encountered in solvent-cast polymeric membranes.
Indirect methods to determine the PSD based on the Young-Laplace equation relating the pressure to the pore diameter include liquid displacement porometry (LDP) and mercury porosimetry. LDP involves progressively displacing a nonvolatile wetting liquid from the largest to the smallest pores by a gas or immiscible liquid under pressure. The pore volume of a given diameter is determined from the displacing fluid flow rate at each pressure. The high pressure required by LDP for UF membranes (typically >30 bar) can cause compaction that alters the PSD and limits it to characterizing pores larger than approximately 10 nm. Mercury porosimetry involves progressively filling the pores with mercury and uses a data-analysis procedure similar to LDP. The PSD determined by mercury porosimetry includes dead-end and continuous pores in contrast to LDP that measures only continuous pores. Owing to the high surface tension of mercury, this technique requires very high pressures.
Indirect methods based on the Kelvin equation relating the vapor pressure to the pore diameter include gas adsorption/desorption (GAD) and permporometry. Both methods involve filling the pores via adsorption and capillary condensation and then reducing the partial pressure to cause progressive desorption from the largest to the smallest pores; the pore volume for each diameter is determined from the amount of gas desorbed. Whereas the PSD determined by GAD includes both continuous pores that extend through the membrane and dead-end pores, permporometry determines only the continuous pores by imposing the simultaneous flow of a non-condensable gas during pore draining. A concentration or temperature gradient can be the driving force for the non-condensable gas flow. Using permporometry is challenging especially for HF membranes because it is necessary to control and measure the non-condensable carrier gas and condensable gas flow rates and the partial pressures across the membrane as well as the temperature. The PSD determined by GAD and permporometry has to be corrected for the t-layer (typically <1 nm). A t-layer forms owing to equilibrium adsorption of gas on the pore walls. The resulting thin adsorbed layer has a maximum thickness on the order of a few nanometers that depends on the particular gas and its partial pressure.
Techniques such as displacement porometry (LDP) and gas adsorption/desorption require relatively expensive dedicated equipment. LDP involves the application of high pressures that can deform the material and thereby its pore-size distribution. Moreover, displacement porometry can characterize only relatively large pores typically greater than 0.01 microns. Gas adsorption/desorption can accurately characterize only relatively small pores typically less than 0.01 microns.
Indirect methods based on the Gibbs-Thompson equation relating the freezing-point temperature to the pore diameter include thermoporometry. This involves gradually increasing the temperature of a frozen liquid-saturated membrane that causes melting progressively from the smallest to the largest pores. The pore diameter and the associated pore volume are obtained from the heat released during solidification or the heat input during melting. A correction is necessary for the smallest pores due to a submicron layer of unfrozen liquid at the pore walls (similar to the t-layer in GAD and permporometry).